\(\mathrm{hv}_{\mathrm{f}}=\mathrm{E}_{\infty}-\mathrm{E}_{5}\)    ..... \((ii)\)

\({\text{E}} \propto \frac{{{{\text{z}}^2}}}{{{{\text{n}}^2}}} \Rightarrow \) \(\frac{{{{\text{E}}_5}}}{{{{\text{E}}_1}}} = {\left( {\frac{1}{5}} \right)^2} = \frac{1}{{25}}\)

\(\operatorname{Eqn}(\mathrm{i}) /(\mathrm{ii}) \Rightarrow \frac{\mathrm{h} v_{\mathrm{L}}}{\mathrm{h} v_{\mathrm{f}}}=\frac{\mathrm{E}_{1}}{\mathrm{E}_{5}}\)

\(\Rightarrow \frac{v_{\mathrm{L}}}{v_{\mathrm{f}}}=\frac{25}{1} \Rightarrow v_{\mathrm{f}}=\frac{v_{\mathrm{L}}}{25}\)